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Temperament; or, the Division of the Octave
Published online by Cambridge University Press: 01 January 2020
Extract
In a previous paper read before the Musical Association on November 2, 1874, a method was developed for the derivation and treatment of a class of systems of tuning, to which the term ‘regular’ was applied—this term being taken to imply that the notes of any such system can be arranged in a continuous series of equal fifths. A notation was described, applicable to written music, by which the position of the notes of such systems in the fundamental series of fifths is defined; and a brief sketch was given of a ‘Generalised Keyboard,’ founded on a principle of ‘symmetrical arrangement,’ by means of which the notes of any such system can be controlled, the fingering of any passage being the same in whatever key it is taken.
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- Research Article
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- Copyright © Royal Musical Association, 1874
References
1 The works of Salinas and Zarlino, in the 16th century, are not accessible to the writer. Salinas is said to hare invented, and Zarlino to have first published, the mean-tone system.Google Scholar
1 This notation refers primarily to perfect fifths and thirds; its development is due to Von Oettingen. Page 438, 3rd edit.Google Scholar
1 Compare ‘Philosophical Magazine,’ Vol. XLIX., p. 352.Google Scholar
1 The opinion above expressed, that equal temperament is the best melodic standard at present, owing to the education of musicians in that system, received remarkable confirmation at the reading of this paper. As will be mentioned later, both the just and mean-tone systems were illustrated by actual performance; and amongst numerous remarks of a similar kind, the following is perhaps the best illustration. The 33rd prelude of Bach's 48 being performed in the mean-tone system, the semitone d# -e was objected to by eminent musicians present. Now this semitone is, theoretically, 1–171, or very nearly ⅙ of an E.T. semitone. The just semitone (difference between perfect third and fourth) is 1,117, or between ⅛ and 
. Hence the mean-tone semitone is nearer to the just semitone than is the E.T. semitone. If, therefore, the diatonic scale were the true standard of melody, the mean-tone semitone should be a little better than the E.T., which would be contrary to the above observation. Again, as to the effect of education. There can be no doubt that in Handel's time all organs in England, and most elsewhere, were tuned to the mean-tone system. Bach abolished this system in Germany, and it has nearly disappeared in England. But there is no doubt that the scales of that system, which afforded good chords, were always looked upon as the best attainable in any manner, the ‘wolf’ due to the limited number of notes being the sole reason for discarding the system. Consequently, the semitone now objected to must formerly have been very generally received as the correct semitone. If musical education in theory were so conducted that the sounds of harmonics, intervals, &c. were studied, as well as numbers and names which have no musical value when taken alone, it might be expected that the practical objection to these intervals, which arises from the exclusive study of equal temperament, would disappear.Google Scholar
1 Organ-builder (address at Mr. Fowler's, 127, Pentonville Road). Mr. Jennings has built an ordinary organ for the writer, and also the large enharmonic harmonium.Google Scholar
1 The Scheibler metronome was exhibited at the meeting, finished all except the graduation. It has been constructed for the writer by Messrs. Tisley & Spiller, 172, Brompton Road.Google Scholar
1 Except, of course, from the tuner's point of view.Google Scholar
1 Smith's Harmonics, Prop. xxii. p. 225.Google Scholar